Simplify the following expression: $a = \dfrac{54z - 18}{6z - 60}$ You can assume $z \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $54z - 18 = (2\cdot3\cdot3\cdot3 \cdot z) - (2\cdot3\cdot3)$ The denominator can be factored: $6z - 60 = (2\cdot3 \cdot z) - (2\cdot2\cdot3\cdot5)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $a = \dfrac{(6)(9z - 3)}{(6)(z - 10)}$ Dividing both the numerator and denominator by $6$ gives: $a = \dfrac{9z - 3}{z - 10}$